Although significant progress has been made for one-dimensional systems,the study of heat conduction in two-dimensional systems is still in its infancy due to the lack of proper materials and the challenge in suspending atomic-thick membrane suitable for thermal transport measurements.Here,we present the experimental studies of thermal conductivity in suspended graphene using thermal bridge method.In submicron suspended single layer graphene(SLG),at T<100K,thermal conductance scale temperature as~T 1.68 and approach the ballistic limit,indicating high sample quality in the measured graphene and that the flexural acoustic phonons(ZA)dominate the thermal conduction [1].This contribution from ZA phonons is found to be systematically suppressed by impurity atoms(Au atoms)on the surface of tri-layer suspended graphene [2].Interestingly and in contrast to bulk materials,when temperature at 300K in SLG,thermal conductivity keeps increasing and remains logarithmic divergence with sample length even for sample lengths much larger than the average phonon mean free path [1].This result is a consequence of the two-dimensional nature of phonons in graphene and possible mechanisms are discussed.